Nuclear magnetic resonance (NMR) has become an indispensable tool in petroleum industry for formation evaluation. This dissertation addresses two problems. • We aim at developing a theory to better understand the phenomena of transverse relaxation in the presence of internal field gradients. • Chracterizing the pore structure of vuggy carbonates. We have developed a two dimensional model to study a system of claylined pore. We have identified three distinct relaxation regimes. The interplay of three time parameters characterize the transverse relaxation in three different regimes. In future work, useful geometric information can be extracted from from SEM images and the pore size distribution analysis of North Burbank sandstone to simulate transverse relaxation using our 2-D clay flake model and study diffusional coupling in the presence of internal field gradients. Carbonates reservoirs exhibit complex pore structure with micropores and macropores/vugs. Vuggy pore space can be divided into separate-vugs and touching-vugs, depending on vug interconnection. Separate vugs are connected only through interparticle pore networks and do not contribute to permeability. Touching vugs are independent of rock fabric and form an interconnected pore system enhancing the permeability. Accurate characterization of pore structure of carbonate reservoirs is essential for design and implementation of enhanced oil recovery processes. However, characterizing pore structure in carbonates is a complex task due to the diverse variety of pore types seen in carbonates and extreme pore level heterogeneity. The carbonate samples which are focus of this study are very heterogeneous in pore structures. Some of the sample rocks are breccia and other samples are fractured. In order to characterize the pore size in vuggy carbonates, we use NMR along with tracer analysis. The distribution of porosity between micro and macro-porosity can be measured by NMR. However, NMR cannot predict if different sized vugs are connected or isolated. Tracer analysis is used to characterize the connectivity of the vug system and matrix. Modified version of differential capacitance model of Coats and Smith (1964) and a solution procedure developed by Baker (1975) is used to study dispersion and capacitance effects in core-samples. The model has three dimensionless groups: 1) flowing fraction (f), 2) dimensionless group for mass transfer (NM) characterizing the mass transfer between flowing and stagnant phase and 3) dimensionless group for dispersion (NK) characterizing the extent of dispersion. In order to obtain unique set of model parameters from experimental data, we have developed an algorithm which uses effluent concentration data at two different flow rates to obtain the fitted parameter for both cases simultaneously. Tracer analysis gives valuable insight on fraction of dead-end pores and dispersion and mass transfer effects at core scale. This can be used to model the flow of surfactant solution through vuggy and fractured carbonates to evaluate the loss of surfactant due to dynamic adsorption.

Nyanza Gulf is a large, shallow and long river-influenced embayment located in northeastern Lake Victoria. The gulf opens to the main lake through the narrow and deep Rusinga Channel, the exchange zone between the two ecosystems with different physical chemical and biogeochemical conditions. The main goals of this study are to characterize physicochemical and nutrient gradients along the gulf-main-lake transect, characterize and quantify the water and nutrient fluxes between the gulf and the main lake, and assess the response of phytoplankton community and photosynthesis to the spatially varying physical and nutrient conditions along the study transect. Between March 2005 and March 2006, measurements of physicochemical profiles as well as nutrient and the phytoplankton community analysis were conductued monthly along the study transect. Additionally, analysis of different surficial sediment phosphorus fractions was done in order to asses the potential role of bottom sediment in contributing to phosphorus enrichment in the lake water column. A box mass balance model was used to calculate the exchange of water and nutrient fluxes between different zones along the study transect and to estimate ecosystem metabolism in the gulf and the channel. Spatial variability in physicochemical and biogeochemical conditions was observed along the study transect, especially between the shallow and river-influenced inner-gulf, the deep and physically active Rusinga Channel, and the main lake, mainly in response to river inputs and varying morphometry along the study transect. The gulf had significantly higher electrical conductivity (EC), turbidity, total nitrogen (TN), and dissolved reactive silica (DRSi) but the levels declined monotonically along the channel in response to mixing with the main lake water. The channel and the main lake had, respectively, significantly higher dissolved inorganic nitrogen (DIN) and soluble reactive phosphorus (SRP) compared to the gulf. Spatial variability in morphometry and exposure to varying wind forcing lead to differential mixing and differential heating and cooling along the transect, resulting in density driven fronts and horizontal exchange of water and nutrients between the gulf and the main lake. Upwelling and downwelling maintained mixing conditions in the channel which consequently influenced nutrient recycling, the light environment and hence affecting phytoplankton community composition and productivity. The net residual water flow from the gulf to the main lake was 36 m3/s but the mixing flux was approximately 20 times higher and both fluxes accounted for a gulf exchange time of 1981 days. The advective and mixing fluxes between the gulf and the main lake resulted in net export of dissolved inorganic phosphorus (DIP; 400 kg P/d) from the main lake into the gulf and net export of DRSi (10 t Si/d) from the gulf into the main lake. In the deep, narrow and physically active Rusinga Channel there was net production of dissolved nutrients whereas in the gulf there was net consumption of dissolved nutrients, which helped to maintain high net ecosystem production (NEP; 566 mg C/m2/d) in the gulf in contrast the channel which showed net heterotrophy. The high NEP in the gulf and the associated high nutrient demand coupled with possibly low SRP to DIN supply ratio lead to P limitation of algal growth in the gulf as indicated by all indicators of nutrient status. This has important implications for management since increased P input into the gulf will translate into increased algal blooms in the gulf and therefore compromise water quality. Spatial variability in physical conditions and nutrient status along the study transect influenced phytoplankton community composition and photosynthesis. The shallow and turbid gulf was dominated by cyanobacteria but diatoms dominated in the channel in response to reduced turbidity and increased physical mixing and nutrient availability (DRSi, SRP). In the main lake seasonal stratification and deep mixing depth favoured both cyanobacteria and diatoms. The phytoplankton community in channel had a higher photosynthetic capacity (Fv/Fm, PBm) compared to both the gulf and the main lake.

In many practical problems in applied sciences, the features of most interest cannot be observed directly, but have to be inferred from other, observable quantities. In particular, many important data acquisition devices provide an access to the measurement of the partial derivatives of a feature of interest rather than sensing its values in a direct way. In this case, the feature has to be recovered through integration which is known to be an ill-posed problem in the presence of noises. Moreover, the problem becomes even less trivial to solve when only a portion of a complete set of partial derivatives is available. In this case, the instability of numerical integration is further aggravated by the loss of information which is necessary to perform the reconstruction in a unique way. As formidable as it may seem, however, the above problem does have a solution in the case when the partial derivatives can be sparsely represented in the range of a linear transform. In this case, the derivatives can be recovered from their incomplete measurements using the theory of compressive sampling (aka compressed sensing), followed by reconstruction of the associated feature/object by means of a suitable integration method. It is known, however, that the overall performance of compressive sampling largely depends on the degree of sparsity of the signal representation, on the one hand, and on the degree of incompleteness of data, on the other hand. Moreover, the general rule is the sparser the signal representation is, the fewer measurements are needed to obtain a useful approximation of the true signal. Thus, one of the most important questions to be addressed in such a case would be of how much incomplete the data is allowed to be for the signal reconstruction to remain useful, and what additional constraints/information could be incorporated into the estimation process to improve the quality of reconstruction in the case of extremely under-sampled data. With these questions in mind, the present proposal introduces a way to augment the standard constraints of compressive sampling by additional information related to some natural properties of the signal to be recovered. In particular, in the case when the latter is defined to be the partial derivatives of a multidimensional signal (e.g. image), such additional information can be derived from some standard properties of the gradient operator. Consequently, the resulting scheme of derivative compressive sampling (DCS) is capable of reliably recovering the signals of interest from much fewer data samples as compared to the case of the standard CS. The signal recovery by means of DCS can be used to improve the performance of many important applications which include stereo imaging, interferometry, coherent optical tomography, and many others. In this proposal, we focus mainly on the application of DCS to the problem of phase unwrapping, whose solution is central to all the aforementioned applications. Specifically, it is shown both conceptually and experimentally that the DCS-based phase unwrapping outperforms a number of alternative approaches in terms of estimation accuracy. Finally, the proposal lists a number of research questions which need to be answered in order to attach strong theoretical guarantees to the practical success of DCS.

<p>This thesis will investigate previously unexplored concepts in magnetic manipulation including controlling the assembly of magnetic and nonmagnetic particles either in bulk fluid or near a substrate. Both uniform glass interfaces and substrates with magnetic microstructures are considered. The main goal of this work is to discuss new strategies for implementing magnetic assembly systems that are capable of exquisitely controlling the positions and orientations of single-component as well as multi-component particle suspensions, including both magnetic and non-magnetic particles. This work primarily focuses on controlling spherical particles; however, there are also several demonstrations of controlling anisotropically shaped particles, such as microrods and Janus colloids. </p><p> Throughout this work, both conventional magnetophoresis and inverse magnetophoresis techniques were employed, the latter relying on ferrofluid, i.e. a suspension of magnetic nanoparticles in a nonmagnetic carrier fluid, which provides a strong magnetic permeability in the surrounding fluid in order to manipulate effectively non-magnetic materials. In each system it was found that the dimensionless ratio between magnetic energy and thermal energy could be successfully used to describe the degree of control over the positions and orientations of the particles. One general conclusion drawn from this work is that the ferrofluid can be modeled with a bulk effective permeability for length scales on the order of 100 nm. This greatly reduces modeling requirements since ferrofluid is a complex collection of discrete nanoparticles, and not a homogenous fluid. It was discovered that the effective magnetic permeability was often much larger than expected, and this effect was attributed to particle aggregation which is inherent in these systems. In nearly all cases, these interactions caused the ferrofluid to behave as though the nanoparticles were clustered with an effective diameter about twice the real diameter.</p><p> The principle purpose of this thesis is to present novel systems which offer the ability to manipulate and orient multi-component spherical or anisotropic particle suspensions near surfaces or in the bulk fluid. First, a novel chip-based technique for transport and separation of magnetic microparticles is discussed. Then, the manipulation of magnetic nanoparticles, for which Brownian diffusion is a significant factor, is explored and modeled. Parallel systems of nonmagnetic particles suspended in ferrofluid are also considered in the context of forming steady state concentration gradients. Next, systems of particles interacting with planar glass interfaces are analyzed, modeled, and a novel application is developed to study the interactions between antigen-antibody pairs by using the self-repulsion of non-magnetic beads away from a ferrofluid/glass interface. This thesis also focuses on studying the ability to manipulate particles in the bulk fluid. First, simple dipole-dipole aggregation phenomenon is studied in suspensions of both nonmagnetic polystyrene particles and endothelial cells. For the sizes of particles considered in these studies, currently accepted diffusion limited aggregation models could not explain the observed behavior, and a new theory was proposed. Next, this thesis analyzed the interactions that exist in multi-component magnetic and nonmagnetic particle suspensions, which led to a variety of novel and interesting colloidal assemblies. This thesis finally discusses the manipulation of anisotropic particles, namely, the ability to control the orientation of particles including both aligning nonmagnetic rods in ferrofluid as well as achieving near-holonomic control of Janus particles with optomagnetic traps. General conclusions of the viability of these techniques are outlined and future studies are proposed in the final chapter.</p> / Dissertation

The goal of this research work is to further the understanding of crystal plasticity, particularly at reduced structural and material length scales. Fundamental understanding of plasticity is central to various challenges facing design and manufacturing of materials for structural and electronic device applications. The development of microstructurally tailored advanced metallic materials with enhanced mechanical properties that can withstand extremes in stress, strain, and temperature, will aid in increasing the efficiency of power generating systems by allowing them to work at higher temperatures and pressures. High specific strength materials can lead to low fuel consumption in transport vehicles. Experiments have shown that enhanced mechanical properties can be obtained in materials by constraining their size, microstructure (e.g. grain size), or both for various applications. For the successful design of these materials, it is necessary to have a thorough understanding of the influence of different length scales and evolving microstructure on the overall behavior. In this study, distinction is made between the effect of structural and material length scale on the mechanical behavior of materials. A length scale associated with an underlying physical mechanism influencing the mechanical behavior can overlap with either structural length scales or material length scales. If it overlaps with structural length scales, then the material is said to be dimensionally constrained. On the other hand, if it overlaps with material length scales, for example grain size, then the material is said to be microstructurally constrained. The objectives of this research work are: (1) to investigate scale and size effects due to dimensional constraints; (2) to investigate size effects due to microstructural constraints; and (3) to develop a size dependent hardening model through coarse graining of dislocation dynamics. A discrete dislocation dynamics (DDD) framework where the scale of analysis is intermediate between a fully discretized (e.g. atomistic) and fully continuum is used for this study. This mesoscale tool allows to address all the stated objectives of this study within a single framework. Within this framework, the effect of structural and the material length scales are naturally accounted for in the simulations and need not be specified in an ad hoc manner, as in some continuum models. It holds the promise of connecting the evolution of the defect microstructure to the effective response of the crystal. Further, it provides useful information to develop physically motivated continuum models to model size effects in materials. The contributions of this study are: (a) provides a new interpretation of mechanical size effect due to only dimensional constraint using DDD; (b) a development of an experimentally validated DDD simulation methodology to model Cu micropillars; (c) a coarse graining technique using DDD to develop a phenomenological model to capture size effect on strain hardening; and (d) a development of a DDD framework for polycrystals to investigate grain size effect on yield strength and strain hardening.

Reservoir fluids are rarely found in homogeneous structures having homogeneous properties. The various elements and processes of the petroleum system result in complex fluid distributions and compositions. A sound understanding of these complexities can avoid disappointing results and costly mistakes when designing the completion and production of the reservoir. The earlier these complexities are understood in the exploration phase, the better are the chances of a successful decision making process in the design phase of the project. Assessing reservoir compartment connectivity is of paramount importance for a optimal field development. Recent technological advances in wireline formation testing and sampling provide asset teams with a new methodology to evaluate in situ fluid properties and reservoir connectivity. After a review of the technology of downhole fluid analysis (DFA), the currently available methods of modeling equilibrated fluid gradients are presented. Fluid composition equilibrium is a stationary state where all components have reached zero mass flux. A reservoir model is designed to simulate numerically equilibration processes over geologic timescales at isothermal conditions where diffusion and gravity are the active mechanisms. A variety of initial conditions and reservoir fluid types is considered. Non-equilibrium fluid gradients and their transient behavior as they evolve towards fluid composition equilibrium are the main interest of this study. The results are compared in case studies, that are available in published literature. The modeling methods allow modeling of vertical and lateral fluid gradients. After a discussion of the cases, this thesis gives recommendations on 1) what fluid properties should be assessed and 2) how many data points are needed to reduce the chance of misinterpretation of non-equilibrium gradients in the presence of faults. To make best use DFA data, the property that exhibits the largest gradient needs to be investigated, as it yields the greatest potential to assess connectivity. The shape of the distribution of fluid composition within a compartment is found to be an important part in investigating reservoir connectivity. During data acquisition efforts should be made to acquire enough data points to reveal this shape. In combination with the presented techniques to identify non-equilibrium conditions, this will optimize DFA data acquisition and maximize the value of the data.

<p>This thesis deals with Computational Fluid Dynamics (CFD)simulations of the flow around delta wings at high angles ofattack. These triangular wings, mainly used in militaryaircraft designs, experience the formation of two vortices ontheir lee-side at large angles of attack. The simulation ofthis vortical flow by solving the Navier-Stokes equations isthe subject of this thesis. The purpose of the work is toimprove the understanding of this flow and contribute to thedesign of such a wing by developing methods that enable moreaccurate and efficient CFD simulations.</p><p>Simulations of the formation, burst and disappearance of thevortices while the angle of attack is changing are presented.The structured flow solver NSMB has been used to get thetime-dependent solutions of the flow. Both viscous and inviscidresults of a 70°-swept delta wing pitching in anoscillatory motion are reported. The creation of the dynamiclift and the hysteresis observed in the history of theaerodynamic forces are well reproduced.</p><p>The second part of the thesis is focusing on automatic meshrefinement and its influence on simulations of the delta wingleading-edge vortices. All the simulations to assess the gridquality are inviscid computations performed with theunstructured flow solver EDGE. A first study reports on theeffects of refining thewake of the delta wing. A70°-swept delta wing at a Mach number of 0.2 and an angleof attack of 27° where vortex breakdown is present abovethe wing, is used as testcase. The results show a strongdependence on the refinement, particularly the vortex breakdownposition, which leads to the conclusion that the wake should berefined at least partly. Using this information, a grid for thewing in the wind tunnel is created in order to assess theinfluence of the tunnel walls. Three sensors for automatic meshrefinement of vortical flows are presented. Two are based onflow variables (production of entropy and ratio of totalpressures) while the third one requires an eigenvalue analysisof the tensor of the velocity gradients in order to capture theposition of the vortices in the flow. These three vortexsensors are successfully used for the simulation of the same70° delta wing at an angle of attack of 20°. Acomparison of the sensors reveals the more local property ofthe third one based on the eigenvalue analysis. This lattertechnique is applied to the simulation of the wake of a deltawing at an angle of attack of 20°. The simulations on ahighly refined mesh show that the vortex sheet shed from thetrailing-edge rolls up into a vortex that interacts with theleading-edge vortex. Finally the vortex-detection technique isused to refine the grid around a Saab Aerosystems UnmannedCombat Air Vehicle (UCAV) configuration and its flight dynamicscharacteristics are investigated.</p><p><b>Key words:</b>delta wing, high angle of attack, vortex,pitching, mesh refinement, UCAV, vortex sensor, tensor ofvelocity gradients.</p>

I implemented and tested the method of Non-Linear Conjugate Gradients (NLCG) to invert magnetotelluric (MT) and radiomagnetotelluric (RMT) data in two dimensions. The forward problem and the objective function gradients were computed using finite-difference methods. The NLCG algorithm was applied to three field data sets to test the performance of the code. It was then compared to the inversion techniques of Occam and damped Occam considering the quality of the output resistivity models and the computation times. The implemented code was further investigated by testing two line search techniques to reduce the objective function along a given search direction. The first line search procedure was constrained to the first Wolfe condition, leading to a rather inexact line search. The second, more thorough line search, was additionally constrained to the second Wolfe condition. Three preconditioners were applied to the NLCG algorithm and their performance was analysed. The first preconditioner was set to the diagonal of the approximate Hessian matrix and updated every 20-th iteration. Preconditioners two and three were updated with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm using the identity matrix and the diagonal of the approximate Hessian matrix as start preconditioners, respectively. The tests showed that the method of NLCG is more efficient pertaining to computation times compared to the Gauss-Newton (GN) based techniques (Occam and damped Occam). For the two smaller data sets that were inverted, the NLCG inversion was two to four times faster than Occam and damped Occam. For the larger data set, the NLCG inversion converged more than one order of magnitude faster than the GN based inversion techniques. This is because GN methods require to evaluate the entire sensitivity matrix to update the model, whereas NLCG only needs to compute a matrix-vector product of the Jacobian. Moreover, expensive operations such as matrix products and direct inversions of linearised systems are avoided by NLCG. A limitation of the NLCG algorithm is that it is prone to converge to local minima due to the fixed Lagrange multiplier that is used in the penalty function. Occam inversion, which determines the optimal Lagrange multiplier as part of the inversion, did not show such problems. The line search tests of the NLCG algorithm showed that an inexact line search yields higher convergence per CPU time than a more exact line search. In accordance to previous studies, preconditioning accelerated the convergence of the NLCG algorithm considerably. The preconditioners updated with the BFGS algorithm achieved highest convergence. Choosing the identity matrix as a start preconditioner led to fast but unstable convergence. The reasons for that could not be determined completely. Taking the diagonal of the approximate Hessian as a start preconditioner instead of the identity matrix led to slower convergence for most of the inversion tests, but convergence could be stabilised. All the tests performed within this project led to a robust implementation of the NLCG algorithm. A default set-up pertaining to line search and preconditioning could be established. However, the NLCG set-up can be adjusted by the user to improve convergence for a specific data set. This makes the algorithm implemented in this thesis more flexible than previously introduced NLCG codes. Preconditioning can certainly still be improved with further tests. Moreover, a future project will be to extend the 2D code to 3D, where NLCG should perform especially well, because the number of model parameters is usually higher in 3D.

Shallow-water hydrothermal vents occur world-wide in regions of volcanic activity. The vents located at Tutum Bay, Ambitle Island, Papua New Guinea are unique in that the vent fluids and surrounding sediments contain some of the highest concentrations of arsenic in a natural system. This study addresses the effects of the vent system on the benthic communities, focusing on the eukaryotes, macrofauna, meiofauna and bacteria. Samples were collected in November 2003 and May/June 2005. Analysis of the 2003 macrofaunal samples indicated that pH, rather than arsenic was influencing the benthic community, and that the hydrothermal influence occurred at a greater distance than expected. Results of more intensive sampling carried out in 2005 are the primary focus of this dissertation. The pore water and sediment characteristics revealed distinct physical habitats corresponding with distance from the vent. There was a trend of decreasing temperature and arsenic concentration and increasing salinity and pH with distance from the vent. The vent sediment was poorly sorted volcanic gravel, while sediments along the transect showed a gradient from fine, well sorted volcanic sands to coarser carbonate sands farther away. The macrofauna showed a trend of increasing diversity with distance from the vent and similar taxa were present in both the 2003 and 2005 samples. The vent community was dominated by the polychaete Capitella cf. capitata. The inner transect from 30 m to 140 m had low diversity. Dominant taxa included thalassinid shrimp and the amphipod Platyischnopus sp.A. The 180 m to 300 m sites had significantly higher diversity. The Danlum Bay reference site had relatively higher diversity than the nearshore transect sites and was dominated by deposit feeding polychaetes. Macrofaunal community structure was influenced by the sediment characteristics, notably by CaCO3 content, sorting and median grain size. The meiofaunal community also showed changes with distance from the vent. Chromadorid nematodes were dominant at the vent site and were a major component of the meiofauna at most sites, along with copepods. The meiofaunal community at the reference site showed greater similarity to the vent community and both sites had low abundances. Nematodes were more abundant than copepods near the vent, but copepods were more abundant farther offshore and at the reference site. Meiofaunal community structure was influenced primarily by the pore water temperature and salinity. Biological interactions with the macrofaunal community through physical disturbance and predation may also influence the meiofaunal community.  The molecular analysis of eukaryotic and bacterial diversity also revealed changes with distance from the vent. The 0 m and reference sites grouped together due to the presence of fungal sequences and the 140 m and 300 m sites grouped together due to a common molluscan sequence. Metazoans and fungi dominated the eukaryote sequences. The most abundant eukaryotic OTUs included fungi matching Paecilomyces sp. and Cladosporium cladosporioides and metazoans matching Viscosia viscosa (Nematoda) and Astarte castanea represented by 24 phyla and was dominated by Actinobacteria and γ-Proteobacteria. More bacterial phyla were present near the vent, while more overall OTUs were found at the intermediate sites along the transect. The most distant site had much lower diversity dominated by Firmicutes. The macrofaunal community had the strongest correlation with environmental variables. Comparison between the meiofauna and the metazoan sequences showed the proportion of nematodes found in both datasets were comparable, but the meiofauna analysis found a higher proportion of arthropods, while the molecular results were disproportionally high for platyhelminthes. Overall, the vents increased the complexity of the system by creating unique habitats. The extreme environment created by the hydrothermal activity maintained the surrounding habitat at an early successional stage colonized by a few opportunistic species. There was a gradation in the benthic communities away from the vent towards a more carbonate based climax community. The low pH environment had an effect on the sediment composition, which in turn influenced the benthic community. These findings can serve as a model for studying the potential effects of ocean acidification and climate change on benthic communities and marine biocomplexity.

The goal of this dissertation is to further our understanding of how spatially heterogeneous landscapes may impact the formation of range boundaries that then aggregate to form large-scale biodiversity patterns. These patterns have been analyzed from many different perspectives by ecologists, evolutionary biologist, and physiologists using a variety of different theoretical, statistical, and mechanistic models. For some species, there is an obvious abrupt change in the environment causing a range boundary. Other environments change gradually, and it is unclear why species fail to adapt and expand their range. The first chapter develops a novel theoretical model of how the establishment of new mutations allows for adaptation to an environmental gradient, when there is no genetic variation for the trait that limits the range. Shallow environmental gradients favor mutations that arise nearer to the range margin, have smaller phenotypic effects, and allow for proportionately larger expansions than steep gradients. Mutations that allow for range expansion tend to have large phenotypic effects causing substantial range expansions. Spatial and temporal variation in climatic and environmental variables is important for understanding species response to climate change. The second chapter uses a mechanistic model to simulate switchgrass (Panicum virgatum L.) productivity across the central and eastern U.S. for current and future climate conditions. Florida and the Gulf Coast of Texas and Louisiana have the highest predicted current and future yields. Regions where future temperature and precipitation are anticipated to increase, larger future yields are expected. Large-scale geographic patterns of biodiversity are documented for many taxa. The mechanisms allowing for the coexistence of more of species in certain regions are poorly understood. The third chapter employs a newly developed wavelet lifting technique to extract scale-dependent patterns from irregularly spaced two-dimensional ecological data and analyzes the relationship between breeding avian richness and four energy variables. Evapotranspiration, temperature, and precipitation are significant predictors of richness at intermediate-to-large scales. Net primary production is the only significant predictor across small-to-large scales, and explains the most variation in richness (~40%) at an intermediate scale. Changes in the species-energy relationship with scale, may indicate a shift in the mechanism governing species richness. / text